for any null vector \(n^{\mu }\) , satisfying \(g_{\mu \nu }(x)n^{\mu }(x)n^{\nu }(x)=0\)  where \(g_{\mu \nu }\)  is the metric tensor of the spacetime manifold. However, over the years, violations of the null energy condition (NEC) [1]}, [2]}, [3]}, [4]}, [5]} have been found in several physical situations. Later, it has been proposed that average null energy condition (ANEC) [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]} is the minimum requirement for the study of BH and it holds for any spacetime, based on the work [13]}. The average null energy condition states that the integral of projection of the matter stress-energy onto the tangent vector of a null geodesic cannot be negative
\(\int _{\gamma }T_{\mu \nu }l^{\mu }l^{\nu }\equiv \int _{\gamma }T_{\mu \nu }(\lambda )l^{\mu }(\lambda )l^{\nu }(\lambda )d\lambda \ge 0,\) 
